question_answer

Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as

Assertion: In Youngs double slit experiment the two slits are at distance d apart. Interference pattern is observed on a screen at D distance fl from the slits. At a point on the screen when it is directly opposite to one of the slits, a dark fringe is observed- Then, the wavelength of wave is proportional to square of distance of two slits. Reason: For a dark fringe intensity is zero.

A)  If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.

B)  If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.

C)  If Assertion is true but Reason is false.

D)  If both Assertion and Reason are false.

Correct Answer: B

Solution :

When dark fringe is obtained at the point opposite to one of the slits then \[{{S}_{1}}P=D\] and        \[{{S}_{2}}P=\sqrt{{{D}^{2}}+{{d}^{2}}}\] \[=D{{\left( 1+\frac{{{d}^{2}}}{{{D}^{2}}} \right)}^{1/2}}\] Path difference \[={{S}_{2}}P-{{S}_{1}}P\] \[=D\left( 1+\frac{{{d}^{2}}}{2{{D}^{2}}} \right)-D\] \[=\frac{{{d}^{2}}}{2D}=\frac{\lambda }{2}\] or  \[\lambda =\frac{{{d}^{2}}}{D}\]   \[\Rightarrow \]\[\lambda \propto {{d}^{2}}\] Now, intensity of a dark fringe is zero.